WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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An Olympic runner who starts a race
with an acceleration of
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4.5 meters per second squared.
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Since they are starting the race, we can
assume that their initial velocity,
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which I guess we call *v naught* ,
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is zero
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and they are gonna be racing
for 2.40 seconds.
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Part (a) asks us for the final speed
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so that will be the initial speed plus
acceleration times time—
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that's equation 52 in chapter 2—
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and so that's 0 meters per second
to start with
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plus 4.5 meters per second
squared acceleration
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multiplied by 2.4 seconds
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giving 10.8 meters per second
will be their final speed.
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And then to sketch a graph of
their position vs. time,
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I used a spreadsheet program called
the LibreOffice
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which is like a free version of Excel
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and it's here
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and I have put in some time's from 0,
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0.5 second, 1 second, 1.5 seconds and so on
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and then the position is this equation
which I'll explain over here;
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we have equation 53 in chapter 2 says
that the final position
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is the initial position plus
initial speed times time
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plus one-half times acceleration
times time squared
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and in this case, they start at position 0
so that's 0.
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They start at rest so the *v naught* is 0
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and so we have the acceleration of
4.5 meters per second squared
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multiplied by this half from the formula
times *t* squared
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that's the formula that is here
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written as 0.5 times 4.5
multiplied by cell *A3*,
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which is the cell right beside
where we are
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in column *A* at the same row
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and that's squared so that's this
caret symbol which is
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'Shift plus 6' and then the number 2
to say that it is to the power of 2.
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So this is one-half times 4.5 times
time squared—that's the position.
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And then we made this chart; time on
the horizontal axis,
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position on the vertical axis
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and we have the units of meters for
position and seconds for time.
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And then I inserted a trend line to
extrapolate between the points
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and then there we go
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that's the graph that's copied here
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and it has this equation.